L. V. Zhukovskaya, “Iterative method for solving nonlinear integral equations describing rolling solutions in string theory”, TMF, 146:3 (2006), 402–409; Theoret. and Math. Phys., 146:3 (2006), 335

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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 146, Number 3, Pages 402–409
DOI: https://doi.org/10.4213/tmf2043 (Mi tmf2043)

This article is cited in 53 scientific papers (total in 53 papers)

Iterative method for solving nonlinear integral equations describing rolling solutions in string theory

L. V. Zhukovskaya

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (187 kB) Citations (53)

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DOI: https://doi.org/10.4213/tmf2043

Abstract: We consider a nonlinear integral equation with infinitely many derivatives that appears when a system of interacting open and closed strings is investigated if the nonlocality in the closed string sector is neglected. We investigate the properties of this equation, construct an iterative method for solving it, and prove that the method converges.

Keywords: string theory, nonlinear integral equation, iterative method.

Received: 21.04.2005
Revised: 17.08.2005

English version:
Theoretical and Mathematical Physics, 2006, Volume 146, Issue 3, Pages 335–342
DOI: https://doi.org/10.1007/s11232-006-0043-3

Bibliographic databases:

Language: Russian

Citation: L. V. Zhukovskaya, “Iterative method for solving nonlinear integral equations describing rolling solutions in string theory”, TMF, 146:3 (2006), 402–409; Theoret. and Math. Phys., 146:3 (2006), 335–342

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This publication is cited in the following 53 articles:

A. Kh. Khachatryan, Kh. A. Khachatryan, A. S. Petrosyan, “O konstruktivnoi razreshimosti odnogo klassa nelineinykh integralnykh uravnenii gammershteinovskogo tipa na vsei pryamoi”, Izv. vuzov. Matem., 2025, no. 3, 89–106
Kh. A. Khachatryan, H. S. Petrosyan, “On qualitative properties of the solution of a boundary value problem for a system of nonlinear integral equations”, Theoret. and Math. Phys., 218:1 (2024), 145–162
A. Kh. Khachatryan, Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya, otsutstviya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi s operatorom tipa Gammershteina — Ctiltesa”, Tr. IMM UrO RAN, 30, no. 1, 2024, 249–269
Kh. A. Khachatryan, H. S. Petrosyan, “Asymptotic Behavior of the Solution for One Class of Nonlinear Integral Equations of Hammerstein Type on the Whole Axis”, J Math Sci, 282:2 (2024), 292
Zahra Keyshams, Khachatur A. Khachatryan, Monire Mikaeili Nia, “Existence and Uniqueness Theorems for One Class of Hammerstein-type Nonlinear Integral Equations”, Lobachevskii J Math, 45:8 (2024), 3580
A. S. Petrosyan, S. M. Andriyan, Kh. A. Khachatryan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa beskonechnoi sistemy nelineinykh dvumernykh uravnenii”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 24:4 (2024), 498–511
Kh. A. Khachatryan, H. S. Petrosyan, “Constructive study of the solvability of one class of nonlinear integral equations with a symmetric kernel”, Siberian Adv. Math., 34:4 (2024), 320–336
H. S. Petrosyan, Kh. A. Khachatryan, “Uniqueness of the Solution of a Class of Integral Equations with Sum-Difference. Kernel and with Convex Nonlinearity on the Positive Half-Line”, Math. Notes, 113:4 (2023), 512–524
A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan, “On nonlinear convolution-type integral equations in the theory of $p$ -adic strings”, Theoret. and Math. Phys., 216:1 (2023), 1068–1081
A.Kh. Khachatryan, Kh.A. Khachatryan, “ON QUALITATIVE PROPERTIES OF A SOLUTION OF ONE CLASS SINGULAR INTEGRAL EQUATIONS ON THE WHOLE LINE WITH ODD NONLINEARITY”, J Math Sci, 271:5 (2023), 597
Kh. A. Khachatryan, A. S. Petrosyan, “O razreshimosti odnogo klassa nelineinykh integralnykh uravnenii Gammershteina na poluosi”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 22:2 (2022), 169–179
Kh. A. Khachatryan, A. S. Petrosyan, “Asimptoticheskoe povedenie resheniya dlya odnogo klassa nelineinykh integralnykh uravnenii tipa Gammershteina na vsei pryamoi”, SMFN, 68, no. 2, Rossiiskii universitet druzhby narodov, M., 2022, 376–391
Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022) (to appear)
Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022), 446–479
Kh. A. Khachatryan, H. S. Petrosyan, S. M. Andriyan, “On the solubility of a class of two-dimensional integral equations on a quarter plane with monotone nonlinearity”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2022, no. 2, 19–38
A. Kh. Khachatryan, Kh. A. Khachatryan, “Ob odnoi sisteme integralnykh uravnenii na vsei pryamoi s vypukloi i monotonnoi nelineinostyu”, Proceedings of NAS RA. Mathematics, 2022, 65
A. Kh. Khachatryan, Kh. A. Khachatryan, “A System of Integral Equations on the Entire Axis with Convex and Monotone Nonlinearity”, J. Contemp. Mathemat. Anal., 57:5 (2022), 311
Kh. A. Khachatryan, H. S. Petrosyan, “Solvability of a certain system of singular integral equations with convex nonlinearity on the positive half-line”, Russian Math. (Iz. VUZ), 65:1 (2021), 27–46
Kh. A. Khachatryan, H. S. Petrosyan, “Alternating bounded solutions of a class of nonlinear two-dimensional convolution-type integral equations”, Trans. Moscow Math. Soc., 82 (2021), 259–271
Kh. A. Khachatryan, A. S. Petrosyan, “O postroenii summiruemogo resheniya odnogo klassa nelineinykh integralnykh uravnenii tipa Gammershteina - Nemytskogo na vsei pryamoi”, Tr. IMM UrO RAN, 26, no. 2, 2020, 278–287

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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